OF EURO TERM STRUCTURE OF CREDIT SPREADS

Transcription

WO R K I N G PA P E R S E R I E S
N O. 3 9 7 / O C TO B E R 2 0 0 4
DETERMINANTS
OF EURO TERM
STRUCTURE OF
CREDIT SPREADS
by Astrid Van Landschoot
WO R K I N G PA P E R S E R I E S
N O. 3 9 7 / O C TO B E R 2 0 0 4
DETERMINANTS
OF EURO TERM
STRUCTURE OF
CREDIT SPREADS 1
by Astrid Van Landschoot 2
In 2004 all
publications
will carry
a motif taken
from the
€100 banknote.
1
This paper can be downloaded without charge from
http://www.ecb.int or from the Social Science Research Network
electronic library at http://ssrn.com/abstract_id=587264.
I would like to thank Jan Annaert, John Crombez, John Fell, Stan Maes, Janet Mitchell, Steven Ongena, Rudi Vander Vennet, and Bas Werker
for helpful comments and suggestions. I am grateful to Deloitte and Touche who helped me to obtain the data. Most of this research has
been conducted during an internship at the European Central Bank and a Marie Curie Fellowship at CentER,Tilburg University.
2 National Bank of Belgium and Ghent University. Correspondance: e-mail: [email protected], tel.: +32 (0)2 221 5333.
© European Central Bank, 2004
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CONTENTS
Abstract
4
Non-technical summary
5
1 Introduction
7
2 Determinants of credit spreads
10
2.1 Risk-free interest rate
12
2.2 Slope of the term structure
12
2.3 Asset value
13
2.4 Asset volatility
14
2.5 Measure of liquidity
14
3 Modeling the term structure of credit spreads
15
3.1 Extended Nelson-Siegel approach
16
3.2 Goodness of fit statistics
18
20
4 Empirical analysis
4.1 Data description
20
4.2 Estimating the term structure of
credit spreads
22
4.2.1 Measures of fit
23
4.2.2 Term structure of credit spreads:
cxtended NS model
24
4.3 Determinants of credit spread changes
25
4.3.1 Model specification and data
25
4.3.2 Estimation results
27
4.3.3 Robustness
31
5 Conclusion
32
References
34
Tables and figures
38
European Central Bank working paper series
55
ECB
Working Paper Series No. 397
October 2004
3
Abstract
In this paper, we investigate the determinants of the Euro term structure of credit
spreads. More specifically, we analyze whether the sensitivity of credit spread changes to
financial and macroeconomic variables depends on bond characteristics such as rating and
maturity. According to the structural models and empirical evidence on credit spreads, we
find that changes in the level and the slope of the default-free term structure, the market
return, implied volatility, and liquidity risk significantly influence credit spread changes.
The effect of these factors strongly depends on bond characteristics, especially the rating
and to a lesser extent the maturity. Bonds with lower ratings are more affected by
financial and macroeconomic news. Furthermore, we find that liquidity risk significantly
increases credit spreads, especially on lower rated bonds.
JEL classification: C22, E45, G15
Keywords: Credit risk, Structural models, Nelson-Siegel
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Non-technical summary
Over the last decade, the analysis of the determinants of credit spreads has gained more
attention for several reasons. The Euro corporate bond market, which lags its US counterpart, has become broader and more liquid. The number and the market value of Euro
corporate bonds have more than doubled over the last decade. The development of the
A and BBB rated market segment has been particularly impressive, coming from virtual
non-existence in early 1998, to account for almost half the individual rated bond issues
outstanding in late 2003. The credit derivatives and structured finance market, which
requires a good understanding of credit risk, has experienced considerable growth over the
last two decades and is expected to grow strongly in the coming years. According to the
Basel II Accord, credit risk models can be used as a basis for calculating a bank’s regulatory capital. To develop and use these models, one needs to make assumptions about what
variables to include and the relation between credit risk and financial and macroeconomic
variables. Finally, central bankers use credit spreads to assess (extract) default probabilities of firms and to assess the general functioning of financial markets. In addition, the
credit spread is often used as a business cycle indicator. Having a better understanding
of credit spreads will help central bankers to extract more precise information from bond
prices/spreads.
In this paper, we investigate the term structure of credit spread changes on investment
grade Euro corporate bonds between 1998 and 2002. We test whether the sensitivity
of credit spread changes to financial and macroeconomic variables significantly depends
on bond characteristics such as rating and maturity. Furthermore, we analyze whether
our empirical results are in line with the predictions of structural credit risk models and
comparable with other studies on US corporate bonds.
Our results indicate that changes in the level and the slope of the default-free term
structure are two important determinants. An increase in the level and/or the slope
significantly reduces credit spread changes. For the higher rating categories (AAA and
AA), the effect of changes in the level and the slope depend on the maturity of the bonds,
that is, the effect first increases and then slightly decreases with the time to maturity. We
find a significant negative relation between the DJ Euro Stoxx returns and credit spread
changes and a significant positive relation between increasing implied volatility of the DJ
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Euro Stoxx and credit spread changes. Although the effects are statistically significant,
the economic importance is much smaller compared to the effect of changes in the defaultfree term structure. The effect of the market return strongly depends on the rating but
not on the maturity of the bonds. Lower rated bonds are much more affected by the
market return. We find evidence for the asymmetric influence of the implied volatility
on credit spread changes, that is, only positive changes in the implied volatility have
a significant impact. Furthermore, the effect of positive changes in the implied volatility
becomes stronger for lower rated bonds but does not depend on the maturity of the bonds.
Liquidity risk, measured as the bid-ask spread, significantly affects all rating categories
and becomes more important for lower rating categories. For AAA and AA rated bonds,
the effect increases with maturity. Finally, we find evidence for mean reversion of credit
spreads for all ratings and maturities. The model explains on average 22% of the variation
in credit spreads as measured by the adjusted R2 . This is comparable with the results for
US corporate bonds.
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1
Introduction
While many studies concentrate on theoretical models for the pricing of corporate bonds
and credit risk, there has been much less empirical testing of these models. Yet, there are
several reasons for investigating the determinants and behavior of credit spreads. First, the
Euro corporate bond market, which lags its US counterpart, has become broader and more
liquid. The number and the market value of Euro corporate bonds have more than doubled
over the last decade. The development of the A and BBB rated market segment has
been particularly impressive, coming from virtual non-existence in early 1998, to account
for almost half the individual rated bond issues outstanding in late 2003. Second, the
credit derivatives market and the structured finance market, which includes collateralized
debt obligations (CDO) and asset-backed securities (ABS), have experienced considerable
growth over the last two decades and are expected to grow strongly in the coming years.
Some structured products such as collateralized bond obligations (CBO) are backed by a
large pool of corporate bonds. This implies that the cash flows (coupon and principal) of
the underlying bonds determine the profitability of these structured products. Therefore,
the creditworthiness of corporate bonds is important for the analysis of these products.
Third, according to the Basel II Accord, credit risk models can be used as a basis for
calculating a bank’s regulatory capital. To develop and use these models, one needs to
make assumptions about what variables to include and the relation between credit risk
and financial and macroeconomic variables such as, for example, the risk-free rate. Finally,
central bankers use credit spreads to assess (extract) default probabilities of firms and to
assess the general functioning of financial markets (credit rationing and sectoral versus
macroeconomic effects). In addition, the credit spread is often used as a business cycle
indicator. Having a better understanding of credit spreads will help central bankers to
extract more precise information from bond prices/spreads.
The contributions of this article are twofold. First, we analyze the determinants of
credit spread changes using a data set of Euro corporate bonds between 1998 and 2002.
As the US has a large and mature corporate bond market, most empirical studies on
the determinants of credit spreads concentrate on US data (see, for example, Longstaff
and Schwartz (1995), Duffee (1998), Collin-Dufresne et al. (2001), Cossin and Hricko
(2001), Elton et al. (2001), and Perraudin and Taylor (2003)). Empirical studies on the
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determinants of European credit spreads are rather limited (see, for example, Boss and
Scheicher (2002)) and mainly focus on time series properties of bond indices. Second,
we analyze the determinants of credit spread changes for bonds with different ratings
and maturities. We test whether the sensitivity of credit spread changes to financial
and macroeconomic variables significantly depends on bond characteristics such as rating
and maturity. Furthermore, we analyze whether our empirical results are in line with
the predictions of structural credit risk models, initiated by Black and Scholes (1973)
and Merton (1974), and comparable with other studies on US corporate bonds. To our
knowledge, this is the first paper to empirically test whether bond characteristics influence
the relation between credit spread changes and macroeconomic and financial variables.
Our analysis is most closely related to that of Collin-Dufresne et al. (2001) on US credit
spreads. While the latter investigates a panel data set of credit spreads on individual
US corporate bonds, this study focuses on the Euro term structure of credit spreads
for different rating categories. The term structure of credit spreads is estimated as the
difference of the term structure of spot rates on Euro corporate and government bonds.
Spot rates, which are estimated by applying an extension of the Nelson-Siegel method on
a data set of individual bond yields, have the advantage that they are not affected by the
coupon rate and much easier to compare than yields to maturity. The disadvantage of
using the term structure of credit spreads is that we solely focus on systematic factors and
not firm-specific factors. However, Collin-Dufresne et al. (2001) conclude that aggregate
factors are much more important than firm-specific factors in explaining credit spread
changes. While Collin-Dufresne et al. (2001) make a distinction between credit spreads
for different rating categories and two maturity classes, we distinguish between credit
spreads for different rating categories and a broad range of maturities. Furthermore, we
test whether the results are significantly different.
The data set consists of weekly observations of prices and yields on 1577 Euro corporate
bonds and 260 AAA government bonds from January 1998 until December 2002. The
bonds in question are those included in Euro bond indices constructed by Merrill Lynch.
The corporate bonds are used to estimate the risky term structure of spot rates, whereas
the government bonds are used to estimated the risk-free term structure of spot rates.
Our results on the estimation of the term structure of credit spreads are as follows: It is
important to take into account the effect of the liquidity risk, the coupon rate, and the
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subrating category. The results show that an extension of the NS model, which includes
these additional factors, produces better estimates of the term structure compared to the
original NS model.
Our results on the determinants of credit spread changes are as follows: According
to the structural credit risk models, we find that changes in the level and the slope of
the default-free term structure, the stock return, and implied volatility of the stock price,
significantly influence credit spread changes. Furthermore, we find that liquidity risk
causes credit spreads to widen. An important conclusion that can be drawn from the
empirical analysis is that the effect of those factors significantly depends on bonds characteristics, especially the rating and to a lesser extent the maturity. Bonds with a lower
rating are often more affected by financial and macroeconomic news. The maturity of the
bond mainly influences the relation between financial and macroeconomic news and credit
spread changes on higher rated bonds (AAA and AA). Finally, we find evidence for mean
reversion of credit spreads for all ratings and maturities.
The model explains on average 22% of the variation in credit spreads as measured by
the adjusted R2 . This is comparable with the results of Collin-Dufresne et al. (2001) for
US corporate bonds. Although the US and the European corporate bond markets differ
significantly in terms of market value and number of bonds, empirical results for bond
markets in both regions are very similar, that is, the impact of financial and macroeconomic
news on credit spread changes is very similar. Our results suggest that the effect of news
on credit spread changes strongly depends more on bond characteristics, especially the
rating.
The paper is organized as follows. Section 2 presents the main determinants of credit
spreads. Some determinants are implied by structural credit risk models, others are deduced from empirical studies. Section 3 gives an overview of the methodology to extract
spot rates (extended Nelson-Siegel model) and four measures of fit. In Section 4, we
first present the data and the estimation results of the term structure of credit spreads.
Then, we empirically analyze the main determinants of credit spread changes for different
(sub)rating categories and maturities. Finally, Section 5 concludes.
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2
Determinants of Credit Spreads
Structural or contingent-claim models, which relate the credit event to the firm’s asset
value and the firm’s capital structure, provides an intuitive framework to assess the main
determinants of credit spreads.1 Since the Merton model is one of the first structural credit
risk models, the literature often refers to it as the representative of the structural models.
Over the last two decades, the model has been extended in several ways by relaxing some
of its restrictive assumptions (see, for example, Geske (1977), Black and Cox (1976), Cox
et al. (1980), Turnbull (1979), Leland (1994, 1998), Longstaff and Schwartz (1995), and
Leland and Toft (1996)). However, the main factors such as the risk-free rate, the asset
value, and the asset volatility and their effect on credit spreads are common to all of
these models. In what follows, we will briefly describe the Merton model and the relation
between credit spreads and factors that are derived from the Merton model. In accordance
with the empirical evidence on the determinants of credit spreads, we also discuss liquidity
risk as a possible determinant.
In the Merton (1974) model, default occurs when the firm’s asset value, VT , falls below
a specified critical value at maturity T . The latter is given by the face value of the firm’s
zerobond debt, L, which is by assumption the only source of debt. The firm’s asset value
process, V , follows an Îto process
dVt
= µdt + σ V dWt ,
Vt
(1)
with µ the drift parameter, σ V the constant volatility, and W a standard Brownian motion.2 In case of default, debt holders receive the amount VT . The value of a default-risky
zero-coupon bond at time T can be written as
D(T ) = min(L, VT ) = L − max(0, L − VT )
1
(2)
The theoretical literature on credit risk pricing can be divided in two broad categories: (1) structural
credit risk models and (2) reduced-form models. The latter do not attempt to model the asset value and
the capital structure of the firm. Instead they specify the credit event as an unpredictable event governed
by a hazard-rate process. Mathematically, these models are more tractable and therefore more suitable for
credit derivatives pricing. For the purpose of this paper, however, we will concentrate on the structural
models.
2
For simplicity, we assume that the payout or dividend ratio equals zero.
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The value of a default-risky zero-coupon bond equals the difference of the value of a defaultfree zero-coupon bond with face value L and the value of European put option written
on the firm’s asset value, with strike price L and exercise date T . The bondholders have
written a put option to the equity holders, agreeing to accept the assets in settlement of
the payment if the value of the firm falls below the face value of the debt. The payoff,
L − VT , is often called the put-to-default. Since V is the sum of the firm’s debt and equity,
the value of the equity can thus be seen as the value of a call option on the firm’s asset
value. Issuing debt is similar to selling the firm’s assets to the bondholders while the
equity holders keep a call option to buy back the assets. Using the put-call parity, this is
equivalent to saying that the equity holders own the firm’s assets and buy a put option
from the bond holders.
Merton (1974) derived a closed-form solution for the price of a defaultable zero-coupon
bond by combining equation (2) with the Black and Scholes formula for the arbitrage price
of a European put option. Having an analytical expression for the price of a defaultable
bond, we can deduce the related credit spread (CR) on a defaultable bond as the difference
between the yield on a defaultable bond, Y d , and the yield on a risk-free bond, Y ,
CR(t, T ) = Y d (t, T ) − Y (t, T ) = −
with
h1,2 (lt , t − T ) =
and
lt =
ln(lt−1 N (−h1 ) + N (h2 ))
,
T −t
(3)
− ln lt ± 21 σ 2V (T − t)
√
,
σV T − t
L exp−r(T −t)
LB(t, T )
.
=
Vt
Vt
N denotes the cumulative probability distribution function of a standard normal. Lt =
LB(t, T ) is the present value of the promised claim (the face value) at the maturity of the
bond (T ) and B(t, T ) represents the value of a unit default-free zero-coupon bond. l is the
leverage ratio, r the continuously compounded risk-free rate, and σ V the volatility of the
firm’s asset value. Equation (3) shows that the credit spread is affected by the risk-free
rate, the asset value, and volatility of the asset value. These factors will be discussed in
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more detail below. In addition, we also discuss the slope of the default-free term structure,
as this variable is implied by the structural models because it is closely related to the riskfree interest rate, and liquidity risk. Finally, we discuss how the leverage and the maturity
of the debt value influences the relation between the credit spread and its determinants.
2.1
Risk-free Interest Rate
We expect a negative relation between the (instantaneous) risk-free rate and the credit
spread. The drift of the risk-neutral process of the value of the assets (see equation (1)),
which is the expected growth of the firm’s asset value, equals the risk-free interest rate. An
increase in the interest rate implies an increase in the expected growth rate of the firm’s
asset value. This will in turn reduce the probability of default and the credit spread (see
Longstaff and Schwartz (1995)). Furthermore, lower interest rates are usually associated
with a weakening economy and thus higher credit spreads.
Simulations based on structural credit risk models show that for firms with moderate
debt levels (l significantly larger than one), the effect of an interest rate change first
increases with the time to maturity (only for short maturities) and then remains constant
(for medium and long maturities). For firm at the brink of default (l close to one), the
effect first decreases with the term to maturity (only for short maturities) and then remains
constant (for medium and long maturities). In general, the effect of an interest rate change
is always stronger for bonds with a higher leverage. Since firms with a higher debt level
often have a lower rating, we expect that the interest rate effect is stronger for bonds with
a lower rating.
2.2
Slope of the Term Structure
The expectations hypothesis of the term structure implies that the slope of the defaultfree term structure, which is often measured as the spread between the long-term and the
short-term rate, is an optimal predictor of future changes in short-term rates over the life
of the long-term bond. As such, an increase in the slope implies an increase in the expected
short-term interest rates. As in the case of the motivation for the risk-free interest rate
above, we expect a negative dependence between changes in the slope of the default-free
term structure and credit spread changes. Litterman and Scheinkman (1991) and Chen
and Scott (1993) document that most of the variations in the term structure can be
explained by changes in the level and the slope.
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Furthermore, the slope of the term structure is often related to future business cycle conditions (see, for example, Estrella and Hardouvelis (1991), Bernard and Gerlach
(1998), and Estrella and Mishkin (1995, 1998)). A decrease in the slope is considered to
be indicators of a weakening economy. A positively sloped yield curve is associated with
improving economic activity, which might in turn increase a firm’s growth rate and reduce
its default probability. This strengthens our expectations of a negative relation between
the slope and the credit spread.
2.3
Asset Value
We expect a negative relation between the credit spread and the firm’s asset value, V .
Firms where the asset value can easily cover the debt value (with a low leverage ratio) are
unlikely to default. An increase in the firm’s asset value (for a given debt value) reduces
the leverage ratio and the value of the put option. As a result, the credit spread will
decrease. Therefore, we expect a negative relation between the firm’s asset value and the
credit spread. According to the Merton type models, the effect of an increase in V on
credit spreads is stronger for bonds with a short term to maturity and for firms with a
high leverage ratio. For bonds with a medium to long term to maturity, the effect is more
or less constant.
Structural models typically assume that the assets of the firm are tradable securities.
In practice, however, the asset value has to be deduced from the balance sheet and is
updated only on an infrequent basis. Therefore, the asset value is usually replaced by the
equity return of publicly traded companies or the return on a stock index. Collin-Dufresne
et al. (2001) conclude that the sensitivity of credit spreads to the S&P 500 return is several
times larger than the sensitivity to firm’s own equity return. Therefore, we mainly focus
on the return on a stock index instead of the return of individual stocks. Similar to the
asset value and in accordance with the empirical findings of Ramaswami (1991), Shane
(1994), and Kwan (1996), we expect a negative relation between the return of a stock
index and the credit spread. Furthermore, the return on a stock index gives an indication
of the overall state of the economy. Several studies (see, for example, Chen (1991), Fama
and French (1989), Friedman and Kuttner (1992), and Guha and Hiris (2002)) show that
credit spreads behave counter-cyclically, that is, credit spreads tend to increase during
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recessions and narrow during expansions. This strengthens our expectation of negative
relation between credit spreads and equity (index) returns. It is very likely that firms
with a high leverage ratio or a smaller capital buffer are more affected by a deterioration
of economic growth. Therefore, we expect that the effect of the return on a stock index is
larger for lower rated bonds.
2.4
Asset Volatility
Equation (3) shows that credit spreads are affected by the volatility of the firm’s asset
value. High asset volatility corresponds with a high probability that the firm’s asset value
will fall below the value of its debt. In that case, it is more likely that the put option will
be exercised and thus, credit spreads will be higher. The effect of a volatility increase is
larger for bonds with a high leverage ratio compared to bonds with a debt value far below
the asset value. For firms with moderate debt levels (l significantly larger than one), the
effect of a change in the volatility first increases with the time to maturity (only for short
maturities) and then remains constant (for medium and long maturities). For firm at the
brink of default (l close to one), the effect first decreases with the term to maturity (only
for short maturities) and then remains constant (for medium and long maturities).
Since the asset value, and thus asset volatility, is only updated on an infrequent basis,
asset volatility is often replaced by equity volatility. As with asset volatility, an increase
in equity volatility increases the probability that the put option will be exercised and
therefore credit spreads will increase (see, for example, Ronn and Verma (1986) and Jones
et al. (1984)). Studies that analyze portfolios of bonds often use the (implied) volatility
of a stock index that is related to the portfolios.3 Campbell and Taksler (2002) find that
equity volatility explains as much variation in corporate credit spreads as do credit ratings.
2.5
Measure of Liquidity
Option models typically used in the structural approach assume perfect and complete
markets where trading takes place continuously. This implies that liquidity risk does not
affect credit spreads. However, Collin-Dufresne et al. (2001), Houweling et al. (2002), and
Perraudin and Taylor (2003) find evidence that liquidity significantly influences credit
3
A basic approach to measure equity volatility is to calculate implied volatility from current option
prices in the market (see, for example, Day and Lewis (1990) and Lamoureux and Lastrapes (1993)).
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spreads (changes). Investors are only willing to invest in less liquid assets compared to
similar liquid assets at a higher premium. If the liquidity risk were similar for government
and corporate bonds, the liquidity premium should be cancelled out when taking the
difference between the two yields. However, government bond markets are larger and more
liquid than corporate bond markets. Therefore, an investor may expect some reward for
the lower liquidity in corporate bond markets.
Amihud and Mendelson (1986) and Easley et al. (2002) argue that liquidity is priced
because investors maximize expected returns net of transactions (or liquidity) costs. Amihud and Mendelson (1986) state that the bid-ask is a natural measure of illiquidity. The
quoted ask price includes a premium for the immediate buying, while the quoted bid
price reflects a concession for immediate sale. Hence, the bid-ask spread measures the
cost of immediate execution. In this paper, we proxy liquidity risk by the bid-ask spread.
Narrowing bid-ask spreads indicate greater liquidity and thus lower credit spreads.
It is not clear whether the effect of liquidity risk should be different for bonds with
different ratings and/or maturities. Houweling et al. (2002) find that the effect of liquidity
risk is stronger for bonds with a lower rating and longer maturities. Perraudin and Taylor
(2003) present similar results for bonds with different maturities.
3
Modeling the Term Structure of Credit Spreads
In accordance with the structural credit risk models, we expect that the relation between
credit spreads changes and macroeconomic and financial variables depends on the leverage
ratio (creditworthiness) of the issuer and the maturity of the bonds. Similar to the leverage
ratio, the rating provides an indication of a firm’s creditworthiness. If a firm’s debt-toassets ratio becomes one, default will occur. At the same time, its rating should move to
the default category.4 Therefore, we use the rating as a proxy for the firm’s leverage ratio.
In order to obtain and easily compare credit spreads on bonds with different ratings
and maturities, we estimate the term structure of credit spreads for AAA, AA, A, and
BBB rated bonds. Moreover, making a distinction between different rating categories also
allows us to more accurately estimate the term structure of credit spreads. The latter
4
Note that in this paper, we focus on investment grade bonds. This means that our sample does not
include firms which are at the brink of default or have a leverage ratio near one.
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is calculated as the difference between the term structure of spot rates on corporate and
government bonds. There are a number of reasons for using the spot rates instead of yields
to maturity. The yield to maturity depends on the coupon rate. The yield to maturity
of bonds with the same maturity but different coupons may vary considerably. As a
results, the credit spread will depend on the coupon rate. Furthermore, by using yields to
maturity, one compares bonds with different duration and convexity. On the other hand,
spot rates are not observable. Therefore, we use an extension of the parametric model
introduced by Nelson and Siegel (1987) to extract the spot rates.
3.1
Extended Nelson-Siegel Approach
The Nelson-Siegel (NS) model offers a conceptually simple and parsimonious description
of the term structure of interest rates. It avoids over-parametrization while it allows
for monotonically increasing or decreasing yield curves and hump shaped yield curves.
Diebold and Li (2002) conclude that the NS method produces one-year-ahead forecasts
that are strikingly more accurate than standard benchmarks. Furthermore, it avoids the
problem in spline-based models to choose the best knot point specification.5
The idea of the NS method is to fit the empirical form of the yield curve with a prespecified functional form for the spot rates, which is a function of the time to maturity of
the bonds.
it (m, θ) = β 0,t + β 1,t
+β 2,t
µ
1 − exp (−mt /τ t )
(−mt /τ t )
(4)
¶
1 − exp (−mt /τ t )
− exp (−mt /τ t ) + εt ,
(−mt /τ t )
¢
¡
with ε ∼ N 0, σ 2 ,
i and m are Nt x1 matrices of spot rates and years to maturity, respectively, with Nt the
number of bonds at time t. θt = (β 0,t , β 1,t , β 2,t , τ t ) is the parameter vector. β 0 represents
the long-run level of interest rates, β 1 the short-run component, and β 2 the medium-term
5
16
For comparison with other methods, see Green and Odegaard (1997).
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component. If the time to maturity goes to infinity, the spot rate converges to β 0 . If
the time to maturity goes to zero, the spot rate converges to β 0 + β 1 . To avoid negative
interest rates, β 0 and β 0 + β 1 should be positive. β 0 can be interpreted as the long-run
interest rate and β 0 + β 1 as the instantaneous interest rate. This implies that −β 1 can be
interpreted as the slope of the yield curve. The curve will have a negative slope if β 1 is
positive and vice versa. β 1 also indicates the speed with which the curve evolves towards
its long-run trend. β 2 determines the magnitude and the direction of the hump or through
in the yield curve. The parameter τ 1 is a time constant that should be positive in order
to assure convergence to the long-term value β 0 . This parameter specifies the position of
the hump or trough on the yield curve.6 The specification in equation (4) is estimated on
a weekly basis on a cross-section of Nt bonds at time t. The sample is divided into four
rating categories j, with j = {AAA, AA, A, and BBB}.
In accordance with Elton et al. (2004), we find that the NS method results in systematic
errors. Therefore, we use an extension of the NS model, which is comparable with Elton
et al. (2004) but not exactly the same, by adding four additional factors to the NS model,
namely liquidity risk, taxation, and plus and minus subrating classifications. First, to
capture differences in liquidity, we add the bid-ask spread as an additional factor (Liq).
If liquidity decreases, bid-ask spreads tend to widen and hence spot rates might go up. A
second reason why spot rates in the same rating category might be different is because of
tax effects. Therefore, we include the difference between the coupon of a bond and the
¡
¢
average coupon rate of the sample C − C . The underlying idea is that low coupon bonds
have a more favorable tax treatment compared to high coupon bonds. Finally, another
reason why spot rates on bonds within a rating category might differ, is that bonds are
not viewed as equally risky. Moody’s and Standard and Poor’s (S&P) both introduced
subcategories within a rating category. While S&P add a plus (+) or a minus (-) sign,
Moody’s adds a number (1,2 or 3) to show the standing within the major rating categories.
Bonds that are rated with a plus (1) or a minus (3) might be considered as having a different
probability of default compared to the flat letter rating (2). Therefore, we include a dummy
6
Svensson (1994) extended the NS model with an additional exponential term that allows for a second
possible hump or trough. However, Geyer and Mader (1999) find that the Svensson method does not
perform better in the form of smaller yield errors in the objective function compared to the NS method.
Furthermore, Bolder and Streliski (1999) conclude that the Svensson model requires approximately four
times as much time in estimation.
ECB
October 2004
17
for the plus subcategory (D_pl) and a dummy for the minus subcategory (D_mi) . For
simplicity, we assume that the additional factors only affect the level of the term structure
and not the slope. Adding four additional factors to the NS model gives
e = β 0,t + β 1,t
it (m, θ)
1 − exp (−mt /τ t )
+ β 2,t
(−mt /τ t )
µ
¶
1 − exp (−mt /τ t )
− exp (−mt /τ t )
(−mt /τ t )
+ β 3,t Liqt + β 4,t (Ct − C t ) + β 5,t D_plt + β 6,t D_mit + e
εt ,
(5)
¢
¡
with e
ε ∼ N 0, σ 2 ,
β 0 , β 1 , β 2 , τ represent the parameters in the original NS model, whereas β 3 , β 4 , β 5 , and
β 6 represent the sensitivities of the spot rates to the additional factors.
e translates in different spot rates and bond prices. ThereEvery set of parameters (θ)
fore, we estimate the parameters as such as to minimize the sum of squared errors between
the estimated yields, yNS , and observed yields to maturity, y, at time t.7
bt = arg min
θ
θt
Nt
X
¡ NS
¢2
yt − yt
i=1
with Nt the number of bonds at time t. We apply maximum likelihood to estimate the
b
parameters, θ.
3.2
Goodness of Fit Statistics
In order to compare the extended model with the original NS method and to test how
well the (extended) NS model describes the underlying data, we estimate three in-sample
measures: (1) the average absolute yield errors (AAE) , (2) the percentage of bonds that
have a yield outside a 95% confidence interval (hit ratio), and (3) the conditional and unconditional frequency of pricing errors. Finally, we examine the out-of-sample forecasting
7
Alternatively, bond prices could be approximated and price errors could be minimized. Because of the
observed heteroskedasticity of fitted price errors and the theoretical relation between prices and interest
rates, most studies weight the price errors by the reverse of the duration of the issues.
18
ECB
October 2004
performance. For each measure, we compare the results of the NS model with those of the
extended NS model.
1. The first measure of goodness of fit is the average absolute yield errors (AAE).
AAEj,t =
Nt ¯
Nt
¯
1 P
1 P
NS
¯(yj,t
− yj,t )¯ =
|εj,t |
Nt j=1
Nt j=1
yt and ytNS are the observed and estimated yields to maturity at time t in rating
category j. Nt is the number of bonds at time t. The higher the AAEj,t the less
good the quality of the fit.
2. The second measure is the percentage of bonds that have an observed yield to maturity outside a 95% confidence interval around the estimated term structure of yields
to maturity. We use the delta method and the maximum likelihood results to obtain
a 95% confidence interval for the term structure of estimated yields to maturity.
´
³
p
p
b − 2 ∗ diag (H) ≤ f (θ) ≤ f (θ)
b + 2 ∗ diag (H) = 95%
Pr f (θ)
0
ϑ f (θ)
with H = ϑ ϑf (θ)
θ Σ ϑθ where Σ denotes the variance-covariance matrix of the estib f (θ)
b denote the estimated yields to maturity according to the
mated parameters θ.
(extended) NS method.
3. As a third measure, we report the conditional frequency of pricing errors. We examine the pricing errors of individual bonds at time t and classify them in three
categories: positive, zero, or negative. Errors are assumed to be zero if the absolute
value of the yield error is below the bid-ask spread. We then look at pricing errors
of these bonds at time t + 1 and report the changes (transition matrix). If pricing
errors are white noise, there should be no clear pattern in the transition matrices.
Bliss (1997) and Diebold and Li (2002) find that regardless of the term structure
estimation method, there is a persistent difference between estimated and actual
bond prices.
4. The previous measures are all in-sample goodness of fit measures. Bliss (1997),
however, concludes that in-sample results may give a distorted view of a method’s
ECB
October 2004
19
performance. Therefore, we also examine the out-of-sample forecasting performance.
Based on the estimation of the parameters, θ at time t, we forecast the term structure
bt ) with k = {1, 2, 4}. We estimate
of the yields to maturity at time t+k, yet+k = f (m, θ
the AAE for the forecasted yields resulting from the (extended) NS model.
4
Empirical Analysis
4.1
Data Description
The data set consists of weekly prices and yields to maturity of individual corporate
and government bonds between January 1998 and December 2002. The corporate and
government bonds in question are included in the EMU Corporate and Government Broad
Market indices, respectively. The latter are based on secondary market prices of bonds
issued in the Euro bond market or in EMU-zone domestic markets and denominated
in Euro or one of the currencies that joined the EMU. Besides bond prices, the data
set contains data on the coupon rate, the time to maturity, the rating, the industry
classification, and the amount issued. Ratings are composite Moody’s and Standard &
Poors ratings. The Merrill Lynch Corporate Broad Market index covers investment-grade
firms. Hence the analysis is restricted to corporate bonds rated BBB and higher. Further,
all bonds have a fixed rate coupon and pay annual coupons. To be included in the
Merrill Lynch indices, corporate bonds should have a minimum size of 100 million Euro
and government bonds of 1 billion Euro. Because the EMU Broad Market indices have
relatively low minimum size requirements, they provide a broad coverage of the underlying
markets.
Several filters are imposed to construct the sample of bonds. First, we exclude unrated
bonds. Second, to minimize the effect of liquidity risk, we exclude all bonds which have less
than one price quote a week on average. Third, to ensure that we consider corporate bonds
backed solely by the creditworthiness of the issuer, we eliminate such bonds as securitized
bonds, quasi & foreign government bonds, and Pfandbriefe. Fourth, as in Duffee (1999),
the data set only includes bonds with at least one year remaining to maturity. These
filters leave us with a data set of 1577 corporate bonds issued by 448 firms. We have 260
AAA rated government bonds.8
8
20
The sample of 260 AAA bonds consists of 101 German, 55 Austrian, 53 French, 37 Dutch, 7 Irish, 4
Spanish and 3 Finish bonds.
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October 2004
We make a distinction between four rating categories: AAA, AA, A, and BBB. From
the 1577 corporate bonds that enter the Merrill Lynch index between January 1998 and
December 2002, 408 bonds have an AAA rating, 509 an AA rating, 484 an A rating, and
176 a BBB rating. If a bond is downgraded to a speculative grade rating (below BBB) or
matured, it is removed from the index. Figure 1 shows the number of bonds in each rating
category over the sample period. While the number of AAA and AA rated bonds has
been stable over the sample period, the number of A and BBB rated bonds has increased
substantially. Between January 1998 and April 2000, the Merrill Lynch included less than
50 BBB rated bonds on average. Moreover, less than half of the BBB rated bonds included
were quoted during that period. Figure 2 presents, for each rating category, the number
of bonds that are not quoted in percentage of the total number of bonds in that rating
category. The results show that before January 2000 less than 50% of the BBB rated
bonds were quoted on a weekly basis. From June 2000, the indicator for BBB rated bonds
has sharply decreased below 20% and converged to a level comparable to higher rated
bonds. Therefore, we will restrict the analysis of BBB rated bonds to the period June
2000-December 2002.
Panel C of Table 2 presents the average yearly rating transition matrix from 1998 to
2002. Each row corresponds to the initial rating and each column corresponds to the
rating after one year. The probability that a bond has the same rating after one year
is 86.5% for BBB and 98.2% for AAA. These results are comparable to the one-year
transition matrices presented by Moody’s Investors Services and Standard and Poor’s
for a data set of predominantly US-based firms (see CreditMetrics, Technical document).
Some probabilities in Panel C are equal to zero. For BBB rated bonds, for example, the
probability of being upgraded to AAA or AA within one year is negligible. The last column
gives the probability that a bond is removed from the index although it has more than
one year to maturity.9 For example, when a bond is downgraded to speculative grade, it
is removed from the index and its rating becomes NA (Not Available). The first column
gives the average number of bonds with an initial AAA, AA, A, or BBB rating.
Panel A of Table 1 presents the average number of corporate bonds in maturity buckets
of 2 or 3 years and for different rating categories. The results show that only few bonds
9
Bonds are normally removed from the Merrill Lynch Broad EMU index one year before maturity.
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October 2004
21
have a maturity beyond 10 years to maturity. Panel B and C of Table 1 show that
the majority of the AAA and AA rated bonds are financials, 96% and 81% respectively,
whereas the majority of the BBB rated bonds are industrials, 84%. A rated bonds are
issued by industrials and financials, 54% and 39% respectively. Utilities issue only few
bonds compared to financials and industrials. Panel A of Table 2 shows that the maturity
of BBB rated bonds varies between 1 and 10 years and between 1 and 22 for A rated
bonds. Although higher rated bonds have on average longer maturities, the number of
bonds beyond 10 years to maturity is limited. The average number of weeks that a bond
is included in the index is 145 weeks.
4.2
Estimating the Term Structure of Credit Spreads
For each rating category, we estimate the term structure of credit spreads by using the
NS and the extended NS model with four additional factors. To motivate the choice of
these four factors, we perform a pooled times series and cross-section analysis of the yield
errors from the NS model
εj = γ 0 + γ 1 D_plj + γ 2 D_mij + γ 3 (Cj −C) + γ 4 Liq,j + η j ,
j = {AAA, AA, A and BBB}
where ε, D_pl, D_mi, C−C, Liq, and η are Kj xT matrices representing yield errors,
dummies for a plus rating, dummies for a minus rating, deviations from the sample average
coupon rate, and bid-ask spreads. Kj is the number of bonds in rating category j and
γ 0 , γ 1 , γ 2 , γ 3 , and γ 4 are the parameters. For each rating category, we use an unbalanced
data set of weekly data from January 1998 until December 2002 (T = 260) , except for BBB
rated bonds (T = 134). The model is estimated using seemingly unrelated regressions
(SUR). Table 3 provides evidence for using four additional factors to the original NS
model. The estimation results confirm that the yield errors from the original NS model
are influenced by the subrating categories (plus, flat or minus), the coupon rate, and
liquidity. All sensitivity coefficients have the expected sign and are significant at the 1%
level, except for the sensitivity of the yield errors of AAA rated bonds to the bid-ask
spreads. Furthermore, the sensitivity of the yield errors to the factors becomes more
important for lower rated bonds.
22
ECB
October 2004
4.2.1
Measures of Fit
Before discussing the results of the term structure estimation, we present the results of four
measures of fit. Figure 7 presents the average yield errors (AAE) for AAA, AA, A, and
BBB rated bonds using the NS model (solid lines) and the extended NS model (dotted
lines). The results indicate that the NS model results in smaller AAE for all rating
categories. Until the first half of 2000, yield errors are similar across rating categories
(except for BBB). From October 2000, yield errors as well as credit spreads in all rating
categories start to diverge. The results indicate that periods of higher credit spreads
coincide with periods of high volatility of yields. This means that the dispersion of credit
spreads within rating category increases during periods of high credit spreads. The latter
are often associated with economic downturns. Panel A of Table 4 present the summary
statistics (mean and standard deviation) of the average yield errors (AAE) from the
(extended) NS method and the results of the t-tests (p-values are given between brackets).
The null hypothesis of equal yield errors of the original and extended NS model is rejected
at 5% level for all rating categories. Panel B of Table 4 shows that, except for AA, yield
errors that result from the extended NS method are on average higher for bonds with
a short to medium term to maturity compared to bonds with a long time to maturity.
Although the difference between yield errors is small, the results indicate that it is easier
to estimate the term structure at the shorter maturity end.
A second measure of fit is the hit ratio, that is, the percentage of bonds that have an
observed yield to maturity outside a 95% confidence interval around the estimated term
structure of yields to maturity (see Panel C of Table 4). Between 2% and 3% of the bonds
have a yield outside a 95% confidence interval if the NS model is applied. The extended
NS model results in much lower hit ratios, between 0.5% and 1.3%. For AA, A, and BBB
rated bonds, most yields outside the confidence interval are above the interval.
The third measure of fit is the transition matrix of the fitted yield errors (see Table
5). For each rating category, fitted yield errors of the NS model (panel A) and extended
NS model (panel B) are classified in three groups: negative, zero, or positive. Column 3
of Table 5 gives the percentage of fitted yield errors in a certain category (unconditional
frequency). Columns 4 to 6 present the percentage of fitted yield errors in a category
ECB
October 2004
23
at time t conditional on the category at time t + 1 (conditional frequency). If errors are
random, the classification at time t should have no effect on the classification at time t + 1.
This means that the unconditional and conditional frequency of being positive should be
similar. However, Table 5 shows that the probability of being positive at time t + 1 if
the yield errors are positive at time t is above 50% for all rating categories. Although
the difference is very small, the persistence of the yield errors is smaller for the extended
NS model. Furthermore, for AAA rated bonds there is a higher probability that the yield
errors fall within the interval between the bid and the ask yield, 29% for AAA rated bond
compared to 7% for BBB rated bonds. If we use the extended NS model even more AAA
rated bonds have yield errors within the bid-ask spread (33% compared to 9%).
Finally, we test the out-of-sample forecasting performance of both the NS and the
extended NS model. We estimate one-week, two-week, and one-month ahead forecasts of
the yields. Table 6 presents the AAE of the original model and the forecasts, for both
the NS and the extended NS model. The AAE of a one-month ahead forecast of AAA
and AA rated bonds are more than double the in sample AAE of the original (extended)
NS model. A one-week ahead forecast results in yield errors that are only slightly higher
than the original model. The forecast yield errors resulting from the extended NS model
are always smaller than those from the NS model.
In general, our results show that the extended Nelson-Siegel model performs better
than the original. Therefore, we will use the latter to estimate the term structure of credit
spreads. However, notice that even for the extended NS model, the dispersion of yields
within a rating category can be substantial, especially for lower rating categories.
4.2.2
Term Structure of Credit Spreads: Extended NS model
Figures 3, 4, 5, and 6 present the credit spreads on AAA, AA, A, and BBB rated bonds
with 3, 5, 7, and 10 years to maturity. The spreads on AA, A, and BBB rated bonds are
a weighted average of the spreads in the subrating categories (plus, flat, and minus). The
weights at time t are the number of bonds in the corresponding subrating category as a
fraction of the total number of bonds in that rating category at time t. Because the data
set includes only few BBB minus rated bonds, we only make a distinction between two
subcategories, namely BBB plus and BBB flat and minus (see Panel B of Table 2). The
disadvantage of having only few bonds in a subrating category is that a single outlier can
significantly influence the results.
24
ECB
October 2004
In accordance with Jones et al. (1984), Sarig and Warga (1989), Fons (1994), and
Jarrow et al. (1997), we find an upward sloping term structure of credit spreads, except
for the beginning of 1998. From the beginning of 2000 until the beginning of 2001, credit
spreads of all rating categories increased. This coincides with a period of zero or negative
growth rate of the OECD leading indicator for the EMU area. In the first quarter of
2001, credit spreads decline as investors believe that the downturn in growth and the rise
in default rates have been priced in bond yields. After September 11, 2001 credit spreads
on AA, A, and BBB rated bond sharply increase. From January 2002, credit spreads
slowly decrease to their level before September 11. At the same time, the growth rate
of the OECD leading indicator become positive, with a peak growth rate in December
2001. From mid 2002, credit spreads in virtually all rating categories widen again. These
evolutions seem to indicate that credit spreads behave counter-cyclically, that is, credit
spreads tend to widen during recessions and narrow during expansions.
Table 7 presents the average and the standard deviation of credit spreads in subrating
categories of bonds with 2 to 10 years to maturity. Bonds with an AA-plus rating have
a credit spread that is on average fifteen basis points lower compared to the AA-minus
rating category. For the A rating category, the difference between the plus and minus
subcategory is even more pronounced. The credit spread on A-minus rated bonds is on
average double the spread on A-plus rated bonds. For the BBB rated bonds, there is a
difference of fifty basis points between the plus rating and the flat and the minus rating.
Credit spreads on AAA and AA rated bonds with 2 years to maturity are on average a few
basis points higher compared to bonds with 3 years to maturity. A possible explanation
is that bonds with 2 years to maturity pay a higher liquidity premium and thus a higher
spread.
4.3
4.3.1
Determinants of Credit Spread Changes
Model Specification and Data
We investigate the determinants of credit spread changes for different types of bonds based
on rating and maturity. We make a distinction between four rating categories, namely
AAA, AA, A, and BBB rated bonds, and nine maturity categories, namely 2 to 10 years
to maturity. For AA and A, we make a distinction between three subrating categories,
ECB
October 2004
25
namely plus, flat, and minus rating, whereas for BBB, we make a distinction between two
subrating categories, namely plus and flat together with minus. The reason is that we
find substantial differences between their credit spreads (see Table 7). Beyond 10 years to
maturity there are not enough bonds to estimate the term structure properly (see Table
1). Therefore, we focus on the term structure of credit spreads up till 10 years to maturity.
The underlying data set consists of weekly data from January 1998 until December
2002. Notice that results for BBB bonds are not directly comparable with the results for
other rating categories since the analysis of the former covers a shorter period (June 2000
until December 2002). In order to analyze the main determinants of credit spread changes
of bonds in rating category j and with years to maturity m, we estimate the following
equation
m
+ α4 4volpt + α5 4volnt
4CRt,j,m = α0 + α1 4i3,t + α2 4islope,t + α3 Rt−1,j
+α6 Liqt−1,j + α7 ∆Liqt,j + α8 (CRt−1,j,m − CR) + ν t,j,m ,
(6)
¡
¢
with ν t,j,m ∼ N 0, σ 2
where Φ = (α0 , α1 , α2 , α3 , α4 , α5 , α6 , α7 , α8 ) is the vector of parameters, and j =(AAA,
AA plus, AA flat, AA minus, A plus, A flat, A minus, and BBB) the rating category.
i3 and islope are the level and the slope of the default-free term structure. As in Duffee
(1998), we define the slope as the spread between the 10-year constant maturity EMU
government bond yield minus the 3 month Euro rate. The level is defined as the 3 month
Euro rate.10
Rjm is a weighted average of the return on the DJ Euro Stoxx Financials and the DJ
Euro Stoxx Industrials. The weights are the number of bonds in rating category j that
are issued in the financial sector, respectively industrial sector, as a fraction of the total
number of financial and industrial bonds in rating category j. The idea is to mimic the
stock price that corresponds to a particular rating category as good as possible. Since the
10
Before January 1999, we define the slope as the spread between the 10-year constant maturity ecu
government bond yield minus the 3 month ecu rate. The level is defined as the 3 month ecu rate.
26
ECB
October 2004
m
AAA rating category mainly consists of financials, RAAA
almost coincides with the return
m
is mainly driven
on the DJ Euro Stoxx Financials. For the BBB rating category, RBBB
by the return on the DJ Euro Stoxx Industrials. We include a one-period lag of Rjm . This
is in accordance with the findings of Kwan (1996) that stocks lead bonds in firm-specific
information, that is, lagged stock returns have explanatory power for current bond yield
changes, while current stock returns are unrelated to lagged bond yield changes.
vol is the implied volatility on the DJ Euro Stoxx. The implied volatility is the average
of the put and the call implied volatility. In accordance with Bekaert and Wu (2000) and
Collin-Dufresne et al. (2001), we test whether the impact of volatility is asymmetric by
making a distinction between positive and negative changes in the implied volatility, 4volp
and 4voln.
Liqj is the average bid-ask spread of the bonds in rating category j. Thus, the average
bid-ask spread is a function of the rating category. The bid-ask spread of BBB rated
bonds is more than double the spread of AAA rated bonds.
Finally, CRt−1,j,m − CR = M R is the level of the lagged credit spread minus the
average in rating category j and maturity range m. This factor should capture the meanreversion of credit spreads, which was first introduced by Longstaff and Schwartz (1995).
If credit spreads evolve around a long-term equilibrium, the sensitivity to the lagged credit
spread should be negative. This means that if credit spreads are high, the changes are
smaller or even negative compared to low credit spread levels.
Weekly data of the explanatory variables are obtained from Datastream and Bloomberg.
We estimate the credit spread model using seemingly unrelated regression (SUR) methodology. The latter has the advantage that it accounts for heteroskedasticity, and contemporaneous correlation in the errors across equations. Furthermore, it allows us to test
whether the sensitivity coefficients for different ratings and maturities are significantly
different.
4.3.2
Estimation Results
We will concentrate on the estimation results for different rating categories (AAA, AA,
A, and BBB) and not subrating categories (plus, flat, and minus). The reason is that
the sensitivity coefficients, Φ, of credit spread changes on bonds with different subratings
ECB
October 2004
27
are very similar.11 Moreover, we cannot reject the null hypothesis that credit spread
changes on bonds with different subratings, for example, AA+ and AA-, react differently
to changes in the explanatory variables. Therefore, we focus on the average credit spreads
on bonds with different rating categories. Panel A to H of Table 8 present the estimation
results for different rating categories and different years to maturity ranging from 2 to 10
years.
We perform Wald tests to analyze whether bonds with different maturities and/or
ratings react in significantly different ways to changes in financial and macroeconomic
variables. Panel A to H of Table 9 present the results of the Wald tests of the following
two null hypotheses
H1 : αs,2yr = αs,3yr = ... = αs,10y = 0, with s = 0, 1, ..., 8,
H2 : αs,2yr = αs,3yr = ... = αs,10y , with s = 0, 1, ..., 8.
Hypothesis 1 (H1) is that the sensitivities of credit spread changes on bonds with 2 to
10 years to maturity to a specific factor s equal zero. If H1 cannot be rejected at the 5%
level, this would mean that a particular factor s does not influence credit spread changes
on bonds with 2 to 10 years to maturity. Hypothesis 2 (H2) is that the sensitivities of
credit spread changes on bonds with 2 to 10 years to maturity to a specific factor s are the
same. If H2 cannot be rejected at the 5% level, this would mean that the maturity does
not influence the effect of financial and macroeconomic news on credit spreads changes.
Table 10 presents the results of the Wald tests of the following hypothesis
H3 : αs,2yr,AAA = αs,2yr,AA , ..., and αs,10yr,AAA = αs,10yr,AA , with s = 0, 1, ..., 8.
Hypothesis 3 (H3) is that the sensitivity of credit spread changes to a particular factor s
is similar for two rating categories, for example, AAA and AA. If H3 is rejected at the 5%
level, this would mean that the rating category does not influence the effect of financial
and macroeconomic news on credit spreads changes.
11
The estimation results for different subrating categories are not presented but are available upon
request.
28
ECB
October 2004
Our first observation is that changes in the level (4i3 ) and the slope (4islope ) of the
default-free term structure are two important determinants of credit spread changes. In
accordance with Longstaff and Schwartz (1995), Duffee (1998), and Collin-Dufresne et al.
(2001) and the Merton type of models, we find a negative relationship between changes in
the level and the slope and credit spread changes. Our results are best comparable with
Collin-Dufresne et al. (2001) as the latter also takes into account other factors besides
the default-free term structure. The sensitivity coefficients α1 and α2 are comparable
with those in Longstaff and Schwartz (1995) and Duffee (1998) but higher than those
in Collin-Dufresne et al. (2001). The null hypothesis that the sensitivities to changes in
the level, α1 , equal zero for the different maturities (H1) is rejected at the 5% level for
AAA and AA and at the 10% level for A. The null hypothesis that the sensitivities to
changes in the slope, α2 , equal zero for the different maturities (H1) is rejected at the 5%
level for all rating categories. For the higher rating categories (AAA and AA), the effect
of changes in the level and the slope depend on the maturity of the bonds, that is, the
effect first increases and then decreases with the time to maturity. For the other rating
categories, the effect of the level and the slope are similar for different maturities. This
is in accordance with our expectations. For low-leveraged firms, the Merton type models
predict that the effect first increases for very short maturities and then remains constant.
However, we mainly focus on bonds with 2 to 10 years to maturity and not on very short
maturities.
We find that the sensitivities to changes in the level and the slope are larger for lower
rated bonds. For example, a 100 basis point increase in 4i3 causes a 6 basis point decrease
in the credit spread changes on AAA rated bonds with 7 years to maturity and a 33 basis
point decrease in the credit spread changes on BBB rated bonds with 7 years to maturity.
This is in accordance with the Merton model. However, the Wald tests cannot reject the
null hypothesis (H3) that the effect is the same for all rating categories (see Table 10).
¡ m ¢
has the expected
In all regressions, the sensitivity to the lagged equity return Rt−1
m
negative sign. If we include Rt−1 , we find that the null hypothesis (H1) that the sensitivities to the lagged market return are simultaneously equal to zero for all maturities
is strongly rejected for all rating categories. However, if we include the current market
return (Rtm ) , H1 is only rejected for A and BBB rated bonds. This result seems to favor
the results of Kwan (1996) who finds that stocks lead bonds in firm-specific information.
ECB
October 2004
29
Lagged stock returns have explanatory power for current credit spread changes. The null
hypothesis that all sensitivities to the lagged market return are similar for all maturities,
can not be rejected at the 5% level for all rating categories. This is in accordance with
our expectations. Furthermore, the results show that the effect of the market return is
larger for bonds with a higher leverage, which is also in accordance with the Merton type
models. A 100 basis point increase of the weekly market return reduces the credit spread
changes on AAA and BBB rated bonds with 7 years to maturity by 0.08 and 0.7 basis
points, respectively. Similar to Longstaff and Schwartz (1995) and Collin-Dufresne et al.
m is economically less important than the effect of
(2001), we find that the effect of Rt−1
changes in the level and the slope of the default-free term structure.
Changes in the implied volatility of the DJ Euro Stoxx (4vol) have the expected
positive sign, which is in accordance with the findings of Campbell and Taksler (2002).
An increase in the implied volatility increases the probability of default and hence causes
a widening of credit spreads. The effect of volatility changes is clearly asymmetric. CollinDufresne et al. (2001) find similar results for credit spreads on US corporate bonds. For
AA, A, and BBB rated bonds, positive changes in the volatility significantly influence
credit spread changes, whereas negative changes do not. For AAA, the results are less
clear. Wald tests show that the effect of the volatility changes does not depend on the
maturity of the bonds. However, the rating is important. In accordance with the Merton
type models, the results show that higher rated bonds are less affected.
As in Collin-Dufresne et al. (2001), Houweling et al. (2002), and Perraudin and Taylor
(2003), liquidity risk, which is measured as the average bid-ask spread, significantly influences credit spread changes on all bonds. The level of the bid-ask spread is significant at
the 5% level in all cases, whereas the changes in the bid-ask spread are only significant for
BBB rated bonds. This shows that credit spread changes are more affected by the level of
liquidity risk than the changes in liquidity risk. This might be due to the fact that higher
rated bonds are more liquid than BBB rated bonds and are not immediately affected by
a change. The bid-ask spread is indeed higher for BBB rated bonds compared to AAA
rated bonds, which shows that BBB rated bonds are less liquid compared to AAA rated
bonds.
In general, the effect of the bid-ask spread becomes stronger for bonds with a lower
rating. An increase of 100 basis points in the bid-ask spread increases the credit spread
30
ECB
October 2004
on AAA and BBB rated corporate bond with 7 years to maturity by 23 and 164 basis
points. For AAA and AA rated bonds, the effect of the bid-ask spread becomes stronger
for bonds with longer maturities.
The credit spread lagged one period significantly influences credit spread changes. H1
is rejected for all rating categories at the 5% level. As expected, we find that a higher
level of the lagged credit spread causes a smaller increase of the credit spread or even
an decrease compared to a lower level. This results provides some evidence for the mean
reversion of credit spreads. The effect does not depend on the maturity of the bonds. The
null hypothesis that all sensitivities are similar across maturities could not be rejected at
the 5% level for all (sub)rating categories (H2).
Finally, the adjusted R2 (last row of each panel) shows that our model explains between
10% and 39% of the variation in credit spreads depending on the rating and time to
maturity. The average adjusted R2 is 23% for AAA rated bonds, 19% for AA rated
bonds, 15% for A rated bonds, and 28% for BBB rated bonds. Our model explains the
most of the variation of credit spreads on bonds with medium maturities. The adjusted
R2 is on average 19% for bonds with 3 and 10 years to maturity and 24% for bonds with
5 and 7 years to maturity.
Although 22% (on average) of the variation of credit spreads can be explained by
factors suggested by the structural credit risk models and empirical studies on the determinants of credit spreads, a large part remains unexplained. In that respect, our results
resembles those of Collin-Dufresne et al. (2001), which find that their model explains on
average 25% of US credit spread changes. Furthermore, they find that the same factors
affect credit spread changes. This seems to indicate that although the US corporate bond
market is broader and more liquid credit spread changes are affected by the same factors.
Furthermore, our results indicate that the effect of financial and macroeconomic news
depends more on the bond characteristics, especially the rating.
4.3.3
Robustness
So far, the level and the slope of the default-free term structure are proxied by the threemonth Euro rate and the difference between the 10-year EMU government bond yield
and the three-month Euro rate. In the NS model, however, the β 0 + β 1 and the −β 1
ECB
October 2004
31
(see equation (4)) are assumed to be the level and the slope of the default-free term
structure. These parameters are estimated on a weekly basis for a sample of 260 AAA
rated government bonds. To check the robustness of our results, we reestimate the credit
spread model (6) and include changes in β 0 + β 1 and −β 1 to proxy for changes in the level
and the slope of the default-free term structure. The correlation between 4 (β 0 + β 1 ) and
the changes in the three month Euro rate is 0.5 while the correlation between 4 (−β 1 ) and
changes in the difference between the 10-year EMU government bond yield and the threemonth Euro rate is 0.4. Although the adjusted R2 slightly decreases, the results (not
show here) are similar to the previous results. Changes in the level and the slope of the
default-free have the expected negative sign. The null hypothesis that the sensitivities to
changes in the level of the default-free term structure are simultaneously equal to zero
for different maturities is rejected at the 1% level for all ratings. The same holds for the
slope effect, except for A minus rated bonds. Including the β 0 + β 1 and the −β 1 slightly
increases the coefficients and the significance of the stock return and the changes in the
volatility of the stock return. The coefficients and the p-values of the bid-ask spread and
the lagged credit spread are not altered.
5
Conclusion
In this paper, we analyze whether the sensitivity of credit spread changes to financial
and macroeconomic variables significantly depends on bond characteristics such rating
and maturity. Using a data set of 1577 investment grade corporate and 260 AAA rated
government bonds, we first estimate the term structure of credit spreads for different
(sub)rating categories by applying an extension of the Nelson-Siegel (NS) method. The
extension includes four additional factors in order to capture differences in liquidity, taxation, and subrating categories.
Then, we analyze changes in the term structure of credit spreads for different (sub)rating
categories. Our results indicate that changes in the level and the slope of the default-free
term structure are two important determinants. An increase in the level and/or the slope
significantly reduces credit spread changes. For the higher rating categories (AAA and
AA), the effect of changes in the level and the slope depend on the maturity of the bonds,
that is, the effect first increases and then slightly decreases with the time to maturity. We
find a significant negative relation between the DJ Euro Stoxx returns and credit spread
32
ECB
October 2004
changes and a significant positive relation between increasing implied volatility of the DJ
Euro Stoxx and credit spread changes. Although the effects are statistically significant,
the economic importance is much smaller compared to the effect of changes in the defaultfree term structure. The effect of the market return strongly depends on the rating but
not on the maturity of the bonds. Lower rated bonds are much more affected by the
market return. We find evidence for the asymmetric influence of the implied volatility
on credit spread changes, that is, only positive changes in the implied volatility have a
significant impact. Furthermore, the effect of positive changes in the implied volatility becomes stronger for lower rated bonds but does not depend on the maturity of the bonds.
Liquidity risk, measured as the bid-ask spread, significantly affects all rating categories
and becomes more important for lower rating categories. While credit spreads on AAA,
AA, and A rated bonds are mainly influenced by the level of the bid-ask spread, credit
spreads on BBB rated bonds are influenced by the level and changes in the bid-ask spread.
This result seems to indicate that liquidity risk itself is more important than changes in
liquidity risk. For AAA and AA rated bonds, the effect increases with maturity. Finally,
we find evidence for mean reversion of credit spreads for all ratings and maturities.
In accordance with Collin-Dufresne et al. (2001), we find that on average 22% of the
variation in credit spread can be explained by the variables suggested by the structural
models and empirical studies. Although the Euro corporate bond market is a relatively
new and expanding market, the results are in line with those for the US corporate bond
market.
ECB
October 2004
33
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ECB
October 2004
37
Table 1: Average Number of Corporate Bonds in Different Rating Categories, Sectors,
and Maturity Ranges
Panel A: Average number of bonds based on rating and maturity
AAA
Total
1-3 years
3-5 years
5-7 years
7-10 years
+10 years
193
65
52
30
32
15
AA
(18)
(9)
(6)
(5)
(4)
(4)
259
72
67
40
67
14
A
(20)
(7)
(11)
(11)
(14)
(3)
236
50
63
45
69
8
(103)
(23)
(30)
(22)
(32)
(3)
BBB∗
115
(53)
24
(21)
42
(21)
32
(7)
17
(5)
-
Panel B: Average number of bonds based on rating and sector
AAA
Total
Financials
Industrials
Utilities
235
225
4
1
AA
(9)
(10)
(1)
(2)
318
258
32
19
A
(28)
(17)
(9)
(5)
265
142
103
16
(112)
(47)
(53)
(13)
BBB∗
131
(63)
8
(7)
111
(51)
8
(3)
Panel C: Average percentage of bonds based on rating and sector
Financials
Industrials
Utilities
AAA
96%
2%
1%
AA
81%
10%
6%
A
54%
39%
6%
BBB∗
6%
84%
6%
Note: This table presents the average number of corporate bonds based on rating and time to maturity
(Panel A) and rating and sector (Panel B). Standard deviations are given between brackets. The average
percentage of bonds based on rating and sector are presented in Panel C. The data set consists of weekly
data from January 1998 until December 2002. ∗ For BBB, the data starts from June 2000.
38
ECB
October 2004
Table 2: Characteristics of the Sample of Bonds
Panel A: Summary statistics of years to maturity and number of weeks
Mean
Stdev
Min
Max
4.9
5.3
5.6
5.1
3.2
3.0
2.8
2.0
1.0
1.0
1.0
1.0
19.9
15.0
21.9
10.2
145
75
Years to Maturity
AAA
AA
A
BBB∗
Number of weeks
Total
Panel B: % of bonds in subrating categories and sectors
AA
A
BBB∗
Subrating categories
Plus
Flat
Minus
24.6%
39.9%
54.5%
42.2%
26.2%
11.4%
33.2%
33.9%
34.1%
Panel C: One year transition matrix
Initial rating
AAA
AA
A
BBB
NA
202
279
214
90
98.2
0.3
1.3
0
1.6
88.9
2.8
0
0.2
10.2
89.9
8.3
0
0
4.5
86.5
0.1
0.6
1.6
5.3
AAA
AA
A
BBB∗
Note: Panel A presents the summary statistics (mean, standard deviation, minimum, and maximum) of
the time to maturity and the number of weeks that a corporate bond is included in the index between
January 1998 and December 2002. Panel B presents the percentage of corporate bonds in the AA, A,
and BBB rating category that have a plus, flat, or minus rating. Panel C presents the probability that a
corporate bond has the same rating or has been up- or downgraded after one year. The latter presents
the average of five yearly transition matrices. ∗ For BBB rated bonds, the analysis covers the period June
2000 until December 2002.
ECB
October 2004
39
Table 3: Pooled Times Series and Cross-section Analysis of Yield Errors
εj = γ 0 + γ 1j D_plj + γ 2 D_mij + γ 3 (Cj −C) + γ 4 Liq,j + η j ,
j = {AAA, AA, A and BBB} ,
where
ε, D_pl, D_mi, (C − C), Liq, and η are Kj xT matrices representing respectively yield
errors, dummies for a plus rating, dummies for a minus rating, deviations from the sample average coupon
rate, bid-ask spreads (liquidity), and errors.
Kj represents the number of corporate bonds in each rating
category j . The model is estimated using seemingly unrelated regressions (SUR).
Constant
AAA
AA
A
BBB∗
-0.01
0.02
-0.03
-0.05
[0.00]
[0.00]
[0.00]
[0.00]
0.03
0.16
0.40
[0.00]
[0.00]
[0.00]
-0.06
-0.10
-0.38
[0.00]
[0.00]
[0.00]
-0.02
-0.02
-0.03
-0.09
[0.27]
[0.00]
[0.00]
[0.00]
Plus rating
Minus rating
Coupon
Liquidity
R2
T (times series)
K (cross-section)
-0.01
-0.09
-0.31
-2.12
[0.00]
[0.00]
[0.00]
[0.00]
0.10
260
395
0.08
260
606
0.14
260
643
0.17
134
202
Note: This table presents the pooled cross-section and times series analysis of yield errors resulting from
the Nelson-Siegel term structure estimations. The analysis covers the period January 1998 until December
2002. p-values are given between brackets. ∗ For BBB rated bonds, the analysis covers the period June
2000 until December 2002.
40
ECB
October 2004
Table 4: Average Absolute Yield Errors
Panel A: Average absolute errors: NS versus extended NS (exNS) model
AAA
Mean
Stdev
t-test
Value
Prob
AA
A
BBB
NS
exNS
NS
exNS
NS
exNS
NS
exNS
8.9
8.0
11.1
10.5
18.0
16.1
51.8
45.0
(2.4)
(2.3)
(1.7)
(1.5)
(8.7)
(7.8)
(27.2)
(25.2)
3.93
4.38
2.72
2.1
[0.00]
[0.00]
[0.01]
[0.04]
Panel B: Average absolute errors of the extended NS Model
AAA
AA
A
BBB
2 yr
3 yr
4 yr
5 yr
6 yr
7 yr
8 yr
9 yr
10 yr
10 yr
8.1
9.8
16.2
67.1
8.8
9.9
17.0
45.2
9.1
10.3
15.5
49.5
9.6
9.4
15.4
45.8
7.4
10.1
16.6
38.4
6.5
11.8
17.4
38.8
5.9
13.8
15.1
54.3
7.8
11.0
15.1
47.2
5.9
10.3
15.5
33.1
5.5
10.5
13.7
31.5
Panel C: % of yields outside a 95% confidence interval (Hit ratio)
NS model
Total
AAA
AA
A
BBB
2.36
2.12
2.85
2.78
Extended NS model
Above
Below
Total
Above
Below
0.88
1.49
2.62
2.52
1.47
0.63
0.23
0.26
1.22
1.04
0.98
0.56
0.50
0.61
0.86
0.56
0.72
0.44
0.13
0.00
Note: Panel A presents the averages and the standard deviations of the absolute yield errors
(AAE yield )
resulting from the term structure estimations using the Nelson-Siegel (NS) and the extended NS model.
For each rating category, we test for equality of the means
(AAE yield ) with a t-test. The latter are
presented in the bottom lines of Panel A. Panel B presents the AAEyield for different maturity ranges.
Panel C presents the percentage of bonds that have a yield outside (above and/or below) a 95% confidence
interval around the estimated term structure. The results in Panel A and C are presented in basis points.
ECB
October 2004
41
Table 5: Transition Matrices of the Fitted Yield Errors
Panel A: Results of the original NS model
Unconditional
Conditional frequency (εt+1 |εt )
εt+1 < 0
εt+1 = 0
εt+1 > 0
frequency (εt )
33.7
87.0
5.4
7.6
AAA
εt < 0
εt = 0
29.2
5.9
85.0
9.1
εt > 0
37.1
7.1
7.0
85.9
AA
εt < 0
εt = 0
εt > 0
43.9
24.2
31.9
89.8
7.7
7.7
4.4
86.6
4.4
5.8
5.7
87.9
A
εt < 0
εt = 0
εt > 0
50.4
13.7
36.0
93.9
10.3
4.6
2.6
81.5
3.3
3.5
8.2
92.1
BBB
εt < 0
εt = 0
εt > 0
60.3
7.1
32.5
96.7
20.7
2.0
2.1
64.2
3.7
1.2
15.1
94.4
Panel B: Results of the extended NS model
Unconditional
Conditional frequency (εt+1 |εt )
εt+1 < 0
εt+1 = 0
εt+1 > 0
frequency (εt )
31.6
85.6
6.0
8.3
AAA
εt < 0
εt = 0
32.6
5.8
86.0
8.2
εt > 0
35.8
7.5
7.7
84.8
AA
εt < 0
εt = 0
εt > 0
41.3
26.0
32.7
89.2
7.9
7.1
5.1
86.0
5.1
5.7
6.1
87.8
A
εt < 0
εt = 0
εt > 0
51.7
15.1
33.2
93.0
11.1
5.7
3.2
78.9
4.6
3.8
9.9
89.6
BBB
εt < 0
εt = 0
εt > 0
54.0
9.3
36.6
92.8
24.1
5.1
3.4
54.9
6.0
3.8
21.0
88.8
Note: The underlying data are the fitted yield errors from the Nelson-Siegel model (panel A) and the
extended NS model (panel B). For each rating category, fitted yield errors are classified in three groups
(pos., zero, neg.) at time t and t+1. The percentages of yield errors in a certain category (unconditional
frequency) are presented in column 3. The percentages of yield errors in a category at time t+1 conditional
on the classification at time t (conditional frequency) are presented in column 4 to 6 in panel A and B.
42
ECB
October 2004
Table 6: Forecasting Performance of the NS and the extended NS model
Panel A: NS model
Original
Forecasts
2 weeks
14.4
(6.5)
1 month
18.8
(9.7)
AAA
Mean
Stdev
8.8
(2.4)
1 week
11.8
(4.5)
AA
Mean
Stdev
11.0
(1.7)
13.7
(3.9)
16.0
(5.7)
20.0
(8.8)
A
Mean
Stdev
18.2
(8.7)
20.0
(9.0)
21.8
(9.4)
24.7
(10.7)
BBB
Mean
Stdev
52.7
(27.1)
53.3
(27.1)
53.9
(27.1)
55.2
(27.3)
8.0
1 week
11.1
Forecasts
2 weeks
13.8
1 month
18.2
(2.3)
(4.6)
(6.6)
(9.8)
10.4
13.1
15.5
19.5
(1.5)
(3.9)
(5.8)
(9.0)
16.2
18.2
20.1
23.2
(7.8)
(8.2)
(8.7)
(10.4)
45.0
47.1
48.1
50.0
(25.2)
(25.1)
(25.2)
(25.4)
Panel B: Extended NS model
Original
AAA
AA
A
BBB
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Note: This table presents the average absolute yield errors of (1) the original model, (2) one-week ahead
forecasts, (3) two weeks ahead forecasts and (4) one month ahead forecasts of the spot rates. Standard
deviations are given between brackets.
ECB
October 2004
43
Table 7: Average Credit Spreads for Different Ratings and Years to Maturity
Years to maturity
2 yr
3 yr
4 yr
5 yr
6 yr
7 yr
8 yr
9 yr
10 yr
20.8
17.0
16.9
18.3
20.2
22.0
23.6
24.9
26.0
(2.6)
(3.4)
(5.2)
(6.7)
(8.0)
(9.0)
(9.8)
(10.4)
(11.0)
23.3
22.6
24.4
27.2
30.1
32.8
35.1
37.1
38.6
(4.1)
(4.3)
(5.9)
(7.7)
(9.2)
(10.2)
(10.9)
(11.4)
(11.6)
27.7
27.0
28.8
31.6
34.5
37.2
39.5
41.5
43.0
(3.6)
(4.8)
(6.8)
(8.6)
(10.1)
(11.3)
(12.1)
(12.6)
(12.9)
37.8
37.1
38.9
41.7
44.6
47.3
49.6
51.6
53.1
(5.9)
(8.5)
(10.6)
(12.4)
(13.8)
(14.9)
(15.7)
(16.2)
(16.6)
38.1
41.6
46.2
50.9
55.2
59.0
62.3
65.1
67.5
(6.3)
(9.9)
(12.9)
(15.1)
(16.8)
(18.1)
(19.0)
(19.8)
(20.4)
53.9
57.4
62.1
66.8
71.1
74.9
78.1
81.0
83.4
(12.4)
(17.6)
(20.7)
(22.8)
(24.3)
(25.4)
(26.2)
(26.9)
(27.4)
77.1
80.6
85.2
89.9
94.2
98.0
101.3
104.1
106.5
(26.9)
(32.0)
(34.9)
(36.7)
(38.0)
(38.8)
(39.5)
(40.0)
(40.5)
BBB+
102.7
104.1
109.9
117.8
126.6
135.7
144.8
153.9
162.9
(24.1)
(27.0)
(30.1)
(31.2)
(31.0)
(30.4)
(29.8)
(29.9)
(31.1)
BBB and
BBB-
152.8
154.2
160.1
167.9
176.7
185.8
195.0
204.1
213.0
(33.9)
(38.6)
(42.0)
(43.1)
(42.9)
(42.2)
(41.6)
(41.3)
(41.9)
AAA
AA+
AA
AA-
A+
A
A-
Note: This table presents the averages and the standard deviations (between brackets) of credit spreads
for different (sub)rating categories and time to maturity. The term structure of credit spreads is estimated
using an extension of the Nelson-Siegel method. The data set covers the period January 1998 until
December 2002, except for BBB rated bonds (June 2000 until December 2002).
44
ECB
October 2004
Table 8: Determinants of Credit Spread Changes: Estimation Results
m
+α6 Liqt−1,j + α7 4Liqt,j + α8 M Rt,j + ν t,j ,
CR is the credit spread, i3 and islope are the level and the slope of the default-free term structure, Rm is
a weighted average of the DJ Euro Stoxx financials and industrials, volp (voln) is the positive (negative)
implied volatility of the DJ Euro Stoxx, Liq is the average bid-ask spread, and M R stands for mean
reversion, that is, a one period lag of the credit spread minus the average credit spread. j stands for
rating category. The model is estimated using Seemingly Unrelated Regressions (SUR). p-values are given
between brackets.
Panel A: AAA rated bonds
2 yr
0.25
3 yr
-0.81
4 yr
-1.21
5 yr
-1.28
6 yr
-1.19
7 yr
-1.04
8 yr
-0.87
9 yr
-0.71
10 yr
-0.56
[0.48]
[0.02]
[0.00]
[0.00]
[0.00]
[0.00]
[0.02]
[0.08]
[0.20]
4i3,t
-2.46
-6.29
-8.05
-8.31
-7.51
-5.98
-4.00
-1.78
0.53
[0.17]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.02]
[0.34]
[0.79]
4islope,t
-3.93
-6.80
-8.46
-9.04
-8.83
-8.15
-7.19
-6.10
-4.99
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
m
Rt−1
-0.03
-0.04
-0.05
-0.06
-0.07
-0.08
-0.08
-0.09
-0.10
[0.24]
[0.13]
[0.04]
[0.01]
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
0.03
0.05
0.07
0.08
0.09
0.08
0.08
0.07
0.06
[0.49]
[0.25]
[0.10]
[0.05]
[0.04]
[0.06]
[0.10]
[0.17]
[0.29]
4volnt
0.10
0.00
-0.02
-0.02
0.00
0.04
0.07
0.11
0.14
[0.03]
[0.91]
[0.58]
[0.66]
[0.91]
[0.41]
[0.13]
[0.04]
[0.01]
Liqt−1
-0.39
1.59
2.35
2.53
2.46
2.29
2.09
1.91
1.77
[0.55]
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.01]
[0.03]
2.09
2.09
3.25
3.92
3.83
3.12
2.04
0.78
-0.51
[0.58]
[0.57]
[0.34]
[0.24]
[0.26]
[0.38]
[0.58]
[0.85]
[0.91]
-0.12
-0.11
-0.10
-0.10
-0.09
-0.09
-0.09
-0.08
-0.08
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
17.0
24.4
31.6
33.7
30.2
24.3
18.5
14.1
11.4
ct
4volpt
4Liqt
MR
R
2
Note: Panel A presents the estimation results for the AAA rated bonds with 2 to 10 years to maturity. The
dependent variables are the credit spread changes on AAA rated bonds. The data set consists of weekly
data from January 1998 until December 2002
(T = 260). The adjusted R2 is presented in percentage.
ECB
October 2004
45
Panel B: AA rated bonds
2 yr
-1.40
3 yr
-2.21
4 yr
-2.34
5 yr
-2.22
6 yr
-2.04
7 yr
-1.88
8 yr
-1.76
9 yr
-1.71
10 yr
-1.72
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
4i3,t
-4.36
-5.86
-5.79
-5.04
-3.99
-2.79
-1.48
-0.13
1.25
[0.03]
[0.00]
[0.00]
[0.00]
[0.02]
[0.11]
[0.41]
[0.95]
[0.56]
4islope,t
-5.14
-6.11
-6.62
-6.65
-6.30
-5.68
-4.90
-4.04
-3.15
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.03]
m
Rt−1
-0.02
-0.04
-0.06
-0.09
-0.11
-0.13
-0.15
-0.17
-0.18
[0.58]
[0.24]
[0.04]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
4volpt
0.12
0.13
0.14
0.15
0.16
0.16
0.15
0.14
0.13
[0.03]
[0.02]
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
[0.01]
[0.03]
4volnt
0.04
0.02
0.02
0.03
0.04
0.04
0.04
0.04
0.04
[0.46]
[0.74]
[0.68]
[0.53]
[0.42]
[0.36]
[0.37]
[0.42]
[0.52]
2.67
4.47
4.90
4.79
4.54
4.29
4.11
4.05
4.11
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
6.84
9.93
9.33
7.74
6.24
5.19
4.66
4.59
4.92
[0.17]
[0.04]
[0.04]
[0.07]
[0.13]
[0.21]
[0.28]
[0.33]
[0.35]
-0.12
-0.11
-0.10
-0.10
-0.10
-0.10
-0.10
-0.10
-0.10
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
19.3
21.7
24.3
25.1
23.4
20.3
16.5
12.9
10.2
ct
Liqt−1
4Liqt
MR
R
2
Note: Panel B presents the estimation results for the AA rated bonds with 2 to 10 years to maturity. The
dependent variables are the credit spread changes on AA rated bonds. The data set consists of weekly
data from January 1998 until December 2002
46
ECB
October 2004
(T = 260). The adjusted R2 is presented in percentage.
Panel C: A rated bonds
2 yr
-2.5
3 yr
-3.6
4 yr
-3.8
5 yr
-3.5
6 yr
-3.2
7 yr
-2.93
8 yr
-2.7
9 yr
-2.5
10 yr
-2.3
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
-8.8
-10.6
-12.2
-12.6
-12.0
-10.7
-8.9
-6.9
-4.9
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.01]
[0.04]
[0.17]
-3.5
-5.3
-8.0
-9.6
-10.0
-9.5
-8.4
-6.9
-5.2
[0.11]
[0.03]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.03]
-0.18
-0.14
-0.12
-0.13
-0.15
-0.19
-0.23
-0.28
-0.33
[0.00]
[0.03]
[0.07]
[0.06]
[0.02]
[0.00]
[0.00]
[0.00]
[0.00]
4volpt
0.24
0.31
0.31
0.29
0.28
0.29
0.32
0.36
0.41
[0.01]
[0.00]
[0.00]
[0.01]
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
4volnt
0.04
0.07
0.09
0.10
0.09
0.07
0.05
0.04
0.02
[0.65]
[0.47]
[0.38]
[0.37]
[0.41]
[0.48]
[0.57]
[0.70]
[0.85]
6.4
9.1
9.8
9.5
8.8
8.0
7.2
6.5
5.9
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
4Liqt
10.29
10.41
14.03
16.40
17.1
16.4
14.9
12.6
10.6
[0.23]
[0.27]
[0.16]
[0.11]
[0.09]
[0.09]
[0.10]
[0.14]
[0.25]
MR
-0.11
-0.10
-0.10
-0.09
-0.09
-0.08
-0.08
-0.07
-0.07
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
13.2
13.6
14.8
15.2
15.1
15.1
15.6
16.7
17.4
ct
4i3,t
4islope,t
m
Rt−1
Liqt−1
R
2
Note: This table presents the estimations results for the A rated bonds. The dependent variables are the
credit spread changes on A rated bonds. The analysis covers the period January 1998 until December
2002. The adjusted R2 is presented in percentage.
ECB
October 2004
47
Panel D: BBB rated bonds
2 yr
-10.7
3 yr
-13.6
4 yr
-14.9
5 yr
-14.9
6 yr
-14.1
7 yr
-12.8
8 yr
-11.3
9 yr
-9.63
10 yr
-7.99
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.01]
[0.04]
4i3,t
-12.0
-14.5
-18.4
-23.1
-27.9
-33.1
-38.8
-45.2
-52.4
[0.52]
[0.21]
[0.08]
[0.05]
[0.03]
[0.02]
[0.02]
[0.02]
[0.02]
4islope,t
-19.9
-14.2
-16.2
-21.4
-27.1
-32.3
-36.8
-40.7
-44.3
[0.12]
[0.08]
[0.03]
[0.01]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
m
Rt−1
-0.77
-0.67
-0.66
-0.67
-0.69
-0.74
-0.79
-0.84
-0.88
[0.02]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.01]
[0.01]
[0.02]
0.40
0.59
0.71
0.82
0.94
1.08
1.25
1.43
1.62
[0.33]
[0.02]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
0.41
-0.22
-0.42
-0.38
-0.23
0.00
0.24
0.49
0.71
[0.33]
[0.40]
[0.09]
[0.14]
[0.44]
[0.99]
[0.52]
[0.26]
[0.15]
15.4
18.5
19.8
19.7
18.4
16.4
14.1
11.5
8.88
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.02]
[0.12]
4Liqt
56.7
43.3
44.6
55.7
70.1
84.3
96.9
107.4
115.7
[0.02]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
MR
-0.17
-0.18
-0.18
-0.18
-0.18
-0.17
-0.17
-0.17
-0.16
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
[0.00]
20.1
17.4
16.1
20.1
26.5
32.5
36.7
38.8
38.9
ct
4volpt
4volnt
Liqt−1
R
2
Note: This table presents the estimation results for the BBB rating category. The dependent variables
are the credit spread changes on BBB rated bonds. The adjusted R2 is presented in percentage. The
analysis covers the period January 1998 until December 2002. Due to unavailability of enough BBB rated
bonds from the start, the analysis for BBB rated bonds covers the period June 2000 until December 2002.
48
ECB
October 2004
Table 9: Restrictions on Coefficients: Wald tests
m
+α6 Liqt−1,j + α7 4Liqt,j + α8 M Rt,j + ν t,j ,
We test the following two hypotheses for each rating category and each coefficient of the model:
αs,2yr = αs,3yr = ... = αs,10y = 0, with s = 1, ..., 7
Hypothesis 2 (H2): αs,2yr = αs,3yr = ... = αs,10y , with s = 1, ..., 7
Hypothesis 1 (H1):
Panel A: AAA rated bonds
H1
H2
χ2
4i3
45.6
4islope
84.4
Rm
19.8
4volp
9.2
4voln
25.4
Liq
22.3
4Liq
4.2
p-value
[0.00]
[0.00]
[0.02]
[0.42]
[0.00]
[0.01]
[0.90]
χ2
38.7
27.5
6.8
4.8
17.9
19.1
3.5
p-value
[0.00]
[0.00]
[0.56]
[0.77]
[0.02]
[0.01]
[0.90]
4islope,t
41.7
[0.00]
9.9
[0.28]
m
Rt−1
31.8
[0.00]
15.0
[0.06]
4volpt
16.6
[0.05]
1.6
[0.99]
4volnt
2.6
[0.98]
1.2
[1.00]
Liqt−1
34.9
[0.00]
20.1
[0.01]
4Liqt
7.0
[0.64]
5.0
[0.76]
4islope,t
22.9
[0.01]
12.5
[0.13]
m
Rt−1
36.1
[0.00]
12.5
[0.13]
4volpt
23.4
[0.01]
7.5
[0.48]
4volnt
2.9
[0.97]
2.5
[0.96]
Liqt−1
27.3
[0.00]
10.7
[0.22]
4Liqt
14.1
[0.12]
10.5
[0.23]
m
Rt−1
32.6
[0.00]
8.6
[0.37]
4volpt
19.8
[0.02]
6.0
[0.65]
4volnt
12.7
[0.18]
12.6
[0.13]
Liqt−1
34.7
[0.00]
10.2
[0.25]
4Liqt
37.8
[0.00]
15.5
[0.05]
Panel B: AA rated bonds
H1
χ2
p-value
H2
χ2
p-value
4i3,t
21.7
[0.01]
18.0
[0.02]
Panel C: A rated bonds
H1
χ2
p-value
H2
χ2
p-value
4i3,t
16.2
[0.06]
6.5
[0.59]
Panel D: BBB rated bonds
H1
χ2
p-value
H2
χ2
p-value
4i3,t
10.5
[0.31]
6.3
[0.62]
4islope,t
18.3
[0.03]
9.5
[0.30]
Note: This table presents the results of Wald tests on two hypothesis: (1) the sensitivities to a factor are
equal to zero for all maturities and (2) the sensitivities to a factor are equal for all maturities. p-values
are given between brackets. Coefficients in bold are significant at the 5% level.
ECB
October 2004
49
Table 10: Comparing different rating categories: Wald tests
m
+ α4 4voldpt + α5 4voldnt
4CRt = α0 + α1 4i3,t + α2 4islope,t + α3 Rt−1,j
+α6 Liqt−1,j + α7 4Liqt,j + α6 RMt−1,j + ν t,j ,
We test the following hypothesis for each pair of rating categories:
Hypothesis:
αs,2yr,AAA = αs,2yr,AA , ...,and αs,10yr,AAA = αs,10yr,AA , with s = 1, ..., 7
AAA versus
AA
A
BBB
AA versus
A
BBB
A versus
BBB
4i3
4islope
Rm
4volp
4voln
Liq
4Liq
10.9
9.3
7.7
9.0
14.5
33.2
6.8
[0.28]
[0.41]
[0.57]
[0.44]
[0.11]
[0.00]
[0.66]
8.5
6.3
20.7
20.6
9.5
26.9
5.7
[0.49]
[0.71]
[0.01]
[0.01]
[0.39]
[0.00]
[0.77]
10.8
13.2
26.9
15.6
11.9
23.7
41.7
[0.29]
[0.15]
[0.00]
[0.08]
[0.22]
[0.00]
[0.00]
11.7
9.4
14.0
17.2
2.6
16.8
13.8
[0.23]
[0.40]
[0.12]
[0.05]
[0.98]
[0.05]
[0.13]
9.5
14.1
29.0
14.2
11.2
30.8
39.2
[0.39]
[0.12]
[0.00]
[0.12]
[0.26]
[0.00]
[0.00]
6.3
10.9
19.6
7.9
11.8
40.4
26.9
[0.71]
[0.28]
[0.02]
[0.54]
[0.22]
[0.00]
[0.00]
Note: This table presents the results of Wald tests on the hypothesis that the sensitivities to a factor are
for bonds with different ratings. p-values are given between brackets. Coefficients in bold are significant
at the 5% level.
50
ECB
October 2004
Figure 1: Number of Bonds in Different Rating Categories
1400
B B B bonds
1200
A bonds
A A bonds
A A A bonds
Number of bonds
1000
800
600
400
200
0
Jan -9 8
Ja n -9 9
Ja n -0 0
Ja n -0 1
Ja n -0 2
Figure 2: Liquidity, % of Index Not Quoted
90
A A A bonds
80
A A bonds
A bonds
70
% of the index without quote
B B B bonds
60
50
40
30
20
10
0
J a n -9 8
Jan -9 9
Ja n -0 0
Ja n -0 1
Ja n -0 2
ECB
October 2004
51
Figure 3: Credit Spreads on AAA Rated Bonds with 3, 5, 7, and 10 Years to Maturity
200
180
3 ye a rs
5 ye a rs
160
7 ye a rs
Credit Spreads (basis points)
1 0 y e a rs
140
120
100
80
60
40
20
0
Jan -9 8
Ja n -9 9
Ja n -0 0
J a n -0 1
Ja n -0 2
Figure 4: Credit Spreads on AA Rated Bonds with 3, 5, 7, and 10 Years to Maturity
200
180
3 y ears
5 y ears
7 y ears
160
Credit spreads (basis points)
1 0 yea rs
140
120
100
80
60
40
20
0
Jan -9 8
52
ECB
October 2004
Ja n -9 9
Jan -0 0
Ja n -0 1
Jan -0 2
Figure 5: Credit Spreads on A Rated Bonds with 3, 5, 7, and 10 Years to Maturity
200
3
5
7
1
180
160
y ea rs
y ea rs
y ea rs
0 y e ars
140
120
100
80
60
40
20
0
J a n -9 8
Ja n -9 9
Ja n -0 0
Ja n -0 1
Ja n -0 2
Figure 6: Credit Spreads on BBB Rated Bonds with 3, 5, 7, and 9 Years to Maturity
300
3 y e a rs
250
5 y e a rs
7 y e a rs
9 y e a rs
200
150
100
50
0
Jan -9 8
Jan -9 9
Ja n -0 0
J a n -0 1
Jan -0 2
ECB
October 2004
53
Figure 7: Average Absolute Yield Errors of Nelson-Siegel (NS) and extended NS model
Average absolute yield errors (basis points)
120
BBB
B B B (e x t.)
A A
A A
( e x t.)
A
A
A A A
A A A (e x t.)
( e x t .)
100
80
60
40
20
0
Jan -9 8
54
ECB
October 2004
Ja n -9 9
Jan -0 0
J a n -0 1
Ja n -0 2
European Central Bank working paper series
For a complete list of Working Papers published by the ECB, please visit the ECB’s website
(http://www.ecb.int)
373 “Technology shocks and robust sign restrictions in a euro area SVAR” by G. Peersman and
R. Straub, July 2004.
374 “To aggregate or not to aggregate? Euro area inflation forecasting” by N. Benalal,
J. L. Diaz del Hoyo, B. Landau, M. Roma and F. Skudelny, July 2004.
375 “Guess what: it’s the settlements!” by T. V. Koeppl and C. Monnet, July 2004.
376 “Raising rival’s costs in the securities settlement industry” by C. Holthausen and
J. Tapking, July 2004.
377 “Optimal monetary policy under commitment with a zero bound on nominal interest rates”
by K. Adam and R. M. Billi, July 2004.
378 “Liquidity, information, and the overnight rate” by C. Ewerhart, N. Cassola, S. Ejerskov
and N. Valla, July 2004.
379 “Do financial market variables show (symmetric) indicator properties relative to exchange
rate returns?” by O. Castrén, July 2004.
380 “Optimal monetary policy under discretion with a zero bound on nominal interest rates”
by K. Adam and R. M. Billi, August 2004.
381 “Fiscal rules and sustainability of public finances in an endogenous growth model”
by B. Annicchiarico and N. Giammarioli, August 2004.
382 “Longer-term effects of monetary growth on real and nominal variables, major industrial
countries, 1880-2001” by A. A. Haug and W. G. Dewald, August 2004.
383 “Explicit inflation objectives and macroeconomic outcomes” by A. T. Levin, F. M. Natalucci
and J. M. Piger, August 2004.
384 “Price rigidity. Evidence from the French CPI micro-data” by L. Baudry, H. Le Bihan,
P. Sevestre and S. Tarrieu, August 2004.
385 “Euro area sovereign yield dynamics: the role of order imbalance” by A. J. Menkveld,
Y. C. Cheung and F. de Jong, August 2004.
386 “Intergenerational altruism and neoclassical growth models” by P. Michel, E. Thibault
and J.-P. Vidal, August 2004.
ECB
October 2004
55
387 “Horizontal and vertical integration in securities trading and settlement” by J. Tapking
and J. Yang, August 2004.
388 “Euro area inflation differentials” by I. Angeloni and M. Ehrmann, September 2004.
389 “Forecasting with a Bayesian DSGE model: an application to the euro area” by F. Smets
and R. Wouters, September 2004.
390 “Financial markets’ behavior around episodes of large changes in the fiscal stance” by
S. Ardagna, September 2004.
391 “Comparing shocks and frictions in US and euro area business cycles: a Bayesian DSGE
approach” by F. Smets and R. Wouters, September 2004.
392 “The role of central bank capital revisited” by U. Bindseil, A. Manzanares and B. Weller,
September 2004.
393 ”The determinants of the overnight interest rate in the euro area”
by J. Moschitz, September 2004.
394 ”Liquidity, money creation and destruction, and the returns to banking”
by Ricardo de O. Cavalcanti, A. Erosa and T. Temzelides, September 2004.
395 “Fiscal sustainability and public debt in an endogenous growth model”
by J. Fernández-Huertas Moraga and J.-P. Vidal, October 2004.
396 “The short-term impact of government budgets on prices: evidence from macroeconomic
models” by J. Henry, P. Hernández de Cos and S. Momigliano, October 2004.
397 “Determinants of euro term structure of credit spreads” by A. Van Landschoot, October 2004.
56
ECB
October 2004

OF EURO TERM STRUCTURE OF CREDIT SPREADS

Transcription

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